This is just a quick heads up. It started to happen in some environments after last Office 2013 patch in mid January 2015. When Outlook 2013 is restarted after patching, it shows only Online Archive, no primary mailbox and user is unable to send e-mails.
It has not yet been defined, however fix is to disable MAPI over HTTPS on affected client, so I suppose it will be network device, which does not understand MAPI over HTTPS protocol.
When changing the below registry key (disable MAPI/HTTP and re-enable RPC/HTTP), the problem disappears:
HKEY_CURRENT_USER\Software\Microsoft\Exchange\MapiHttpDisabled = 1 DWORD
Install Exchange 2013 CU7.